Related papers: Bing doubling and the colored Jones polynomial
We describe rules for computing a homology theory of knots and links in $\mathbb{R}^3$. It is derived from the theory of framed BPS states bound to domain walls separating two-dimensional Landau-Ginzburg models with (2,2) supersymmetry. We…
The bivariate $P$- and $Q$-polynomial structures of association schemes based on attenuated spaces are examined using recurrence and difference relations of the bivariate polynomials which form the eigenvalues of the scheme. These…
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…
Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a…
We review the Reshetikhin-Turaev approach to construction of non-compact knot invariants involving R-matrices associated with infinite-dimensional representations, primarily those made from Faddeev's quantum dilogarithm. The corresponding…
For any virtual link $L = S \cup T$ that may be decomposed into a pair of oriented $n$-tangles $S$ and $T$, an oriented local move of type $T \mapsto T'$ is a replacement of $T$ with the $n$-tangle $T'$ in a way that preserves the…
In this note, we compute the cyclotomic expansion formula for colored Jones polynomial of double twist knots with an odd number of half-twists $\mathcal{K}_{p,\frac{s}{2}}$ by using the Kauffman bracket skein theory. It answers a question…
Quantum invariants like the colored Jones polynomial are algebraic in nature but are conjectured to detect important information about the geometry of links. In this thesis we explore these connections using an enhanced version of the RT…
In this paper, we find an elementary approach for double sums where the inner sum is binomial but incomplete. We apply our core identity and its relatives to double sums involving famous numbers such as harmonic numbers, Fibonacci numbers,…
This paper defines versions of the Jones polynomial and Khovanov homology by using several maps from the set of Gauss diagrams to its variant. Through calculation of some examples, this paper also shows that these versions behave…
Two photon correlations are studied for a binary star system. It is investigated how the differential Hanbury Brown and Twiss (HBT) approach can be used in order to determine orbital parameters of a binary star.
It has long been known that the quadratic term in the degree of the colored Jones polynomial of a knot is bounded above in terms of the crossing number of the knot. We show that this bound is sharp if and only if the knot is adequate. As an…
The notion of a Bing cell is introduced, and it is used to define invariants, link groups, of 4-manifolds. Bing cells combine some features of both surfaces and 4-dimensional handlebodies, and the link group \lambda(M) measures certain…
We describe a simple formula for computing the Heegaard Floer multicurve invariant of double tangles from the Heegaard Floer multicurve invariant of knot complements. A comparison with a similar multicurve invariant for Conway tangles in…
A {\em blink} is a plane graph with a bipartition (black, gray) of its edges. Subtle classes of blinks are in 1-1 correspondence with closed, oriented and connected 3-manifolds up to orientation preserving homeomorphisms \cite{lins2013B}.…
We propose a new method for numerical calculation of link plynomials for knots given in 3 dimensions. We calculate derivatives of the Jones polynomial in a computational time proportional to $N^{\alpha}$ with respect to the system size $N$…
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…
It is known that the homogeneous coordinate ring of a Grassmannian has a cluster structure, which is induced from the combinatorial structure of a plabic graph. A plabic graph is a certain bipartite graph described on the disk, and there is…
We construct a quantum algorithm to approximate efficiently the colored Jones polynomial of the plat presentation of any oriented link L at a fixed root of unity q. Our construction is based on SU(2) Chern-Simons topological quantum field…
The trace of $n$-framed surgery on a knot in $S^3$ is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded 2-sphere…